Greatest Common Factor of 289/40, 806/36, 221/75

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 289/40, 806/36, 221/75

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 289/40,806/36,221/75

Given fractions are 289/40,806/36,221/75

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 289,806,221

Greatest Common Factor of Numerators i.e. GCF of 289,806,221 is 1 .

LCM of Denominators means LCM of 40,36,75 as per the given fractions.

LCM of 40,36,75 is 1800 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 289,806,221

GCF of Fractions 289/40,806/36,221/75 is 1/1800

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 289,806,221 By Matching Biggest Common Factor Method

Greatest Common Factor of 289,806,221 By Matching Biggest Common Factor Method

Factors of 289

List of positive integer factors of 289 that divides 289 without a remainder.

1,17,289

Factors of 806

List of positive integer factors of 806 that divides 806 without a remainder.

1,2,13,26,31,62,403,806

Factors of 221

List of positive integer factors of 221 that divides 221 without a remainder.

1,13,17,221

Greatest Common Factor

We found the factors 289,806,221 . The biggest common factor number is the GCF number.
So the greatest common factor 289,806,221 is 1.

Lets's calculate LCM of 40,36,75

2 40, 36, 75
2 20, 18, 75
3 10, 9, 75
5 10, 3, 25
2, 3, 5

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 2 x 3 x 5 = 1800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1800

Therefore, the GCF of Fractions 289/40,806/36,221/75 is 1/1800

Least Common Multiple of 40,36,75 with GCF Formula

Least Common Multiple of 40,36,75 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 40,36,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,36,75) = 1

common factors(in case of two or more numbers have common factors) = 60

GCF(40,36,75) x common factors =1 x 60 = 60

LCM(40,36,75) = ( 40 × 36 × 75 ) / 60

LCM(40,36,75) = 108000 / 60

LCM(40,36,75) = 1800


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 289/40, 806/36, 221/75

1. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

2. What is the GCF of Fractions for 289/40, 806/36, 221/75?

Answer: GCF of Numerators as per given numbers 289/40, 806/36, 221/75 is

GCF of Numerators i.e. for 289,806,221 is 1

LCM of denominators i.e. for 40,36,75 is 1800.

Thus, GCF of Fractions is 1/1800.Finally, GCF of Fractions for 289/40, 806/36, 221/75 is 1/1800.